# Calculus of One Real Variable

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Joydeep Dutta
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/109104124)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/109104124)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course intend to develop a thorough understanding of the fundamental aspects of calculus of single variable which is fundamental tool in Sciences, Engineering and Economics.

Intended audience: First year engineering, science and economics students with mathematics as main course.Prerequisites : Basic mathematics till 12th standard

## Lectures

1. [Introduction to Numbers](https://invisiblenetwork.ai/learn/nptel/109104124/bb9d5b3b7283) (YouTube)
2. [Countability and Uncountability](https://invisiblenetwork.ai/learn/nptel/109104124/ad05d2b450be) (YouTube)
3. [Examples of Irrational numbers](https://invisiblenetwork.ai/learn/nptel/109104124/daa852fc033b) (YouTube)
4. [Functions](https://invisiblenetwork.ai/learn/nptel/109104124/f15eb581eb4e) (YouTube)
5. [Limits of Functions-I](https://invisiblenetwork.ai/learn/nptel/109104124/030dba91c1bb) (YouTube)
6. [Limit of Functions- II](https://invisiblenetwork.ai/learn/nptel/109104124/f95506453259) (YouTube)
7. [Continuous Functions](https://invisiblenetwork.ai/learn/nptel/109104124/e1e70d506946) (YouTube)
8. [Intermediate Value Theorem](https://invisiblenetwork.ai/learn/nptel/109104124/0ed1d4cbf91b) (YouTube)
9. [Maximum Value Theorem](https://invisiblenetwork.ai/learn/nptel/109104124/3cd287eb6010) (YouTube)
10. [Supremum and Infimum](https://invisiblenetwork.ai/learn/nptel/109104124/50d2571e00e8) (YouTube)
11. [Derivative of a Function](https://invisiblenetwork.ai/learn/nptel/109104124/0a0bf3dd94fa) (YouTube)
12. [Rules of Differentiation](https://invisiblenetwork.ai/learn/nptel/109104124/d50723ab4429) (YouTube)
13. [Maxima and Minima](https://invisiblenetwork.ai/learn/nptel/109104124/3521fcbec19c) (YouTube)
14. [Rolle's Theorem and Lagrange Mean Value Theorem (MVT)](https://invisiblenetwork.ai/learn/nptel/109104124/de0528056e46) (YouTube)
15. [Monotonic Functions and Inverse Functions](https://invisiblenetwork.ai/learn/nptel/109104124/422469107936) (YouTube)
16. [Newton’s Method for solving Equations](https://invisiblenetwork.ai/learn/nptel/109104124/da829e58ada6) (YouTube)
17. [Optimization Problems](https://invisiblenetwork.ai/learn/nptel/109104124/9953bf12f9a6) (YouTube)
18. [Integration-I : In the style of Newton and Leibnitz](https://invisiblenetwork.ai/learn/nptel/109104124/eab2542c42ef) (YouTube)
19. [Integration-II : In the spirit of Newton and Leibnitz](https://invisiblenetwork.ai/learn/nptel/109104124/1e35171dbded) (YouTube)
20. [Integration-III : Newton and Leibnitz Style](https://invisiblenetwork.ai/learn/nptel/109104124/ecf40f857bdd) (YouTube)
21. [Integration theory of Riemann-I](https://invisiblenetwork.ai/learn/nptel/109104124/c24ec7179f14) (YouTube)
22. [Integration theory of Riemann-II](https://invisiblenetwork.ai/learn/nptel/109104124/473c1b1b0f42) (YouTube)
23. [Integration Rule](https://invisiblenetwork.ai/learn/nptel/109104124/3aef46bf4e38) (YouTube)
24. [Fundamental Theorem of Calculus (in Riemann style)](https://invisiblenetwork.ai/learn/nptel/109104124/5eb79de7c585) (YouTube)
25. [The Kurzweil-Henstock Integral (K-H Integral)](https://invisiblenetwork.ai/learn/nptel/109104124/0fdd15fc36dc) (YouTube)
26. [Calculating Indefinite Integrals](https://invisiblenetwork.ai/learn/nptel/109104124/de08004f3d81) (YouTube)
27. [Improper Integral-I](https://invisiblenetwork.ai/learn/nptel/109104124/b13628a002b1) (YouTube)
28. [Improper Integral-II](https://invisiblenetwork.ai/learn/nptel/109104124/4794a5d8091b) (YouTube)
29. [Application of Definite Integral-I](https://invisiblenetwork.ai/learn/nptel/109104124/3993cbc447f3) (YouTube)
30. [Application of definite Integral-II](https://invisiblenetwork.ai/learn/nptel/109104124/9db42914f4e6) (YouTube)
31. [Application of definite Integral-III](https://invisiblenetwork.ai/learn/nptel/109104124/34cf5de5c2c5) (YouTube)
32. [Application of definite Integral-III](https://invisiblenetwork.ai/learn/nptel/109104124/c210e98e646a) (YouTube)
33. [Numerical Integration-I](https://invisiblenetwork.ai/learn/nptel/109104124/0bf3f589aff5) (YouTube)
34. [Numerical Integration-II](https://invisiblenetwork.ai/learn/nptel/109104124/4474251acd13) (YouTube)
35. [Sequences](https://invisiblenetwork.ai/learn/nptel/109104124/237a973b06d9) (YouTube)
36. [Sequence (continued)](https://invisiblenetwork.ai/learn/nptel/109104124/1d0a83f6525e) (YouTube)
37. [Infinite Series](https://invisiblenetwork.ai/learn/nptel/109104124/9d1df369d9d2) (YouTube)
38. [infinite series (continued)](https://invisiblenetwork.ai/learn/nptel/109104124/517d44eb3f9c) (YouTube)
39. [Taylor's Theorem, other issues and end of the course-I](https://invisiblenetwork.ai/learn/nptel/109104124/d53ff69557f4) (YouTube)
40. [Taylor's Theorem, other issues and end of the course-II](https://invisiblenetwork.ai/learn/nptel/109104124/3d733f4e6a17) (YouTube)